Continuous-time deadbeat control for sampled-data systems

When a continuous-time linear system is discretized using a hold, stability of poles are preserved. However, the transformations of zeros are much more complicated and the number of the zeros increases in some cases in the discretization process. This paper is concerned with the zeros of a sampled-data model resulting from a continuous-time multivariable system which is not decouplable by static state feedback and has all of the relative degrees one. Two cases of a zero-order hold and a fractional-order hold are treated. An approximate expression of the zeros is given as power series expansions with respect to a sampling period in the zero-order hold case. Further, the limiting zeros are analyzed in the fractional-order hold case. Then, the advantage of the fractional-order hold to the zero-order hold is discussed from the viewpoint of stability of the zeros.

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Stability analysis for complicated sampled-data systems via descriptor remodelling

IMA Journal of Mathematical Control and Information ◽

10.1093/imamci/dny031 ◽

2018 ◽

Vol 36 (4) ◽

pp. 1347-1373 ◽

Cited By ~ 3

Author(s):

Jun Zhou ◽

Ketian Gao ◽

Xinbiao Lu

Keyword(s):

Stability Analysis ◽

Frequency Domain ◽

Continuous Time ◽

Transfer Functions ◽

Open Loop ◽

Spectral Features ◽

Data Systems ◽

Sampled Data ◽

Digital Controllers ◽

Lifting Technique

AbstractA new stability analysis technique is developed in this paper for complicated sampled-data systems with both analogue and digital controllers, by frequency-domain equivalence in the continuous-time sense and time-delayed descriptor (or singular) state-space realization remodelling. The technique is independent of the lifting technique and thus employs neither structural nor spectral features of any discrete-time transfer functions of continuous-time plants. The suggested criteria are stated with frequency-domain conditions, involving neither open-loop unstable poles nor contour/locus-orientation-related encirclements counting. The criteria are implementable graphically with locus plotting or numerically tractable without locus plotting. The descriptor remodelling advantages are further exploited in surmounting infinite dimensionality and structural/spectral features unavailability in multi-rate and time-delayed sampled-data systems. Numerical examples are included to illustrate the main results.

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Control System Analysis and Design Via the “Second Method” of Lyapunov: II—Discrete-Time Systems

Journal of Basic Engineering ◽

10.1115/1.3662605 ◽

1960 ◽

Vol 82 (2) ◽

pp. 394-400 ◽

Cited By ~ 172

Author(s):

R. E. Kalman ◽

J. E. Bertram

Keyword(s):

Discrete Time ◽

Continuous Time ◽

System Analysis ◽

Companion Paper ◽

Data Systems ◽

Sampled Data ◽

Analysis And Design ◽

Continuous Time Systems ◽

Time Systems ◽

Second Method Of Lyapunov

The second method of Lyapunov is applied to the study of discrete-time (sampled-data) systems. With minor variations, the discussion parallels that of the companion paper on continuous-time systems. Theorems are stated in full but motivation, proofs, examples, and so on, are given only when they differ materially from their counterparts in the continuous-time case.

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